CN105069240B - Survey station layout intelligent optimization method of spatial measurement positioning system - Google Patents

Abstract

A survey station optimization deployment problem is one of important problems in use of a spatial measurement positioning system. The present invention provides a survey station layout intelligent optimization method of a spatial measurement positioning system, so that an optimized survey station layout can fully cover a tested area under certain costs and a requirement of measurement accuracy can be met. According to the present invention, a proper positioning error model is established from three aspects of constraint analysis, optimization objective, and optimization means, a multi-goal optimizing function is defined, and survey station layout optimization of the spatial measurement positioning system is implemented by using a practical intelligent optimization algorithm. According to the survey station layout intelligent optimization method of a spatial measurement positioning system, a survey station network optimization deployment problem of the spatial measurement positioning system in an engineering application is effectively resolved. As a quantity of survey stations increases, the method has good expansibility, provides a new method for a multi-station networking measurement layout optimization problem based on an angle intersection principle, and has important theoretical value and practical significance.

Description

A kind of space measurement positioning system survey station layout intelligent optimization method

Technical field

The invention belongs to industry spot large scale three-dimensional coordinate measurement technical field, particularly to multistation networking measuring system Survey station intelligent optimization dispositions method and in particular to a kind of space measurement positioning system survey station layout intelligent optimization method.

Background technology

In heavy construction measurement, not only physical dimension is big for measurand, and relative accuracy has high demands and (is better than 10ppm), keypoint quantity to be measured is many, and multiple measuring task are simultaneously deposited, and it is big to be affected by the external environment, therefore measuring method and making Measurer all has particularity.Network type multistation measuring system has balancing a survey scope, certainty of measurement and measurement efficiency three The great potential of contradiction between person, is that the accurate measurement in Large-Scale Equipment manufacture process provides strong technical support, is big chi The study hotspot of very little fields of measurement and important development direction.

Space measurement positioning system (workspace Measuring and Positioning System, wMPS) is one Plant new network type multistation measuring system, this systematic survey range can carry out unlimited expansion in theory, and can achieve tested Space multiple spot real-time parallel measurement.Abroad earliest to this systematic study is Arcsecond company of the U.S. (having been incorporated into Nikon), It is referred to as indoor GPS or iGPS.Its composition is main to include emitter, pick-up probe, scale, wireless receiving electronic devices and components And computer controlling center.Bath university of Britain and German Karlsruhe university geodesic survey institute have been carried out greatly to iGPS Amount Performance Evaluation experiment and dynamic tracking applied research.Some Domestic colleges and universities and research institution are also substantial amounts of to the system have been Theoretical research and prototype experiment.

Because space measurement positioning system is to realize measurement of coordinates under the collective effect of many survey stations, the property of therefore single survey station Synergism between energy and each survey station is two critical aspects of impact systematic entirety energy.The synergism of many survey stations is not Only rely upon the measurement model of single survey station, the model that crosses of many survey stations, and be distributed and there is substantial connection with survey station space geometry. Additionally, increasing with survey station number, system use cost also being gradually increased, in order to by cost control in rational scope, Suitable survey station number is selected to be also problems faced in engineering practice.The research impact to system position error for the survey station layout, Optimize survey station network structure, for improving system accuracy, reduces cost provides theory support, provides cloth for engineering practice simultaneously Stand guidance, be the major issue that space measurement positioning system faces.

In terms of existing survey station network layout optimization research, the Claudia of the German karr Si Luer Institute of Technology Depenthal et al. is studied to the layout of four cell site's compositions in iGPS system.Employ in an experiment Box layout and C layout, devises 17 standard points, and the measurement result of experimental result and API laser tracker is compared, experimental result Show to compare with Box type layout, the error distribution of c-type layout is more uneven.Aachen, Germany polytechnical university lathe and manufacture work Demeester of the Robert Schmitthe of journey institute and Nikon-Metrology company et al. is to iGPS in robot Several representative configurations during locating and tracking have carried out simulation analysis, and result shows, the measurement effect of standard type is best.Also has scholar Start with from wMPS network topology and position error relation, have studied the impact to position error for the representative configuration, test result indicate that O_4 type layout overall measurement accuracy highest.It is all that minority station or specified arrangement are carried out above to the research of survey station network topology Research and contrast experiment, do not have general expansion when facing more survey station networkings measurement, and the selection of layout are limited to Representative configuration mode, lacks motility and versatility when measuring environment becomes complexity.

Also there is scholar to adopt standard genetic algorithm with wMPS system position error, area coverage and use cost conduct simultaneously Object function is laid out optimizing, but this method exists and easily makes result be absorbed in local optimum, the problems such as convergence rate is slow, leads Cause survey station can not reach optimal location, the raising of impact space measurement positioning system performance.

Content of the invention

The technical problem to be solved is to overcome the deficiencies in the prior art, lacks adaptability in engineering practice Wider array of survey station layout optimization method, and not by impact system layout parameters consider the problems such as, propose a kind of base Office of portion intelligent optimization method in the space measurement positioning system survey station of improved adaptive GA-IAGA.In space measurement positioning system, Set up system position error, the multiple target numerical relationship model of area coverage and use cost.Considering different model dimensions not In the case of same, with method for normalizing, the layout optimization problem of space measurement positioning system be converted into single objective programming and ask Topic, and carry out global optimizing with Revised genetic algorithum, obtain optimum survey station dispositions method.

The present invention adopts the technical scheme that a kind of space measurement positioning system survey station layout intelligent optimization method, its feature It is, in space measurement positioning system, in order to obtain the survey station layout of optimum, set up by survey station position error, coverage And the multiple target numerical relationship model of use cost composition, i.e. survey station layout optimized mathematical model, with method for normalizing by sky Between the layout optimization problem of measurement and positioning system be converted into single-object problem, and obtained optimum using improved adaptive GA-IAGA Survey station layout.

Comprise the following steps that：

Step 1), in space orientation measuring system, set up survey station layout optimized mathematical model, fixed including system

Position error model, system ovelay range model, cost model；

Step 2), with method for normalizing, the layout multi-objective optimization question of space measurement positioning system is converted into monocular Mark optimization problem；

Step 3), using improved adaptive GA-IAGA, survey station layout Optimized model is solved.

Described step 1) in,

System Model of locating error to set up process as follows：

In space orientation measuring system, mainly include cell site, receptor, scale, omnidirectional's vector rod, it is directly seen It is measured as optical plane from zero scan to the time of measured point.Under the local coordinate system of cell site, temporal information and horizontal angle And vertical angle can set up one-to-one functional relationship.Therefore for each measurement of cell site, following formula is all had to set up：

T in formula_n=(x_n,y_n,z_n), n=1,2 ... N are expressed as n-th cell site's zero coordinate, P=(x_T,y_T,z_T) Represent point coordinates to be measured, R_nIt is the distance of floor projection range coordinate initial point under n-th cell site's coordinate system for the measured point.

If m_niRepresent the i ＆ lt horizontal angle of n-th cell site and the measurement of vertical angle, then have：

m_i=f_i(T₁,T₂,...T_n, P) and=m_ni+ε_ni, n=1,2 ... N

By f_iFunction, through Taylor series expansion and after removing all nonlinear components, obtains azimuth angle error propogator matrix H, It is expressed as:

In formulaFor measured point to n-th cell site's initial point away from From,For measured point floor projection to n-th cell site's initial point distance, now correspond to Measurement error covariance matrix be Vm：

In formulaWithRepresent horizontal angle and vertical angular measurement variance respectively.It is weighted locating according to covariance matrix Reason, now location estimation covariance matrix D is：

D=(H^TVm^-1H)^-1

According to matrix D, arrangement manner is for any point P spatially_kGDOP (precision geometry dilution gfactor) represent For：

Layout optimization to all survey stations is to reach the highest positioning precision to measured point, then above formula can be derived as：

O₁=GDOP_pk.

Described step 1) in,

System area coverage model to set up process as follows：

Define cell site two optical plane inclination angle and be respectively φ₁And φ₂, make φ_max=max (φ₁,φ₂) it is then right with Z axis Claim axle, cone angle is 2 φ_maxTwo inverted cone up and down be cell site's laser plane scan blind spot.Receptor and cell site away from From difference, the pulsewidth of light pulse will change, and therefore receptor would operate in limited distance range.

The measured target P dispensing at random on horizontal surface areas β ≡ 0_i, its coordinate is (x_i,y_i), for any survey station T_j, Measured target P_iWith any survey station T_jBetween Euclidean distance be：

Therefore only need to d (P_i,T_j) receptor effective working distance [LR_min,LR_max] between.And for having one Determine the plane domain of height H, the azimuth coverage that cell site can measure is represented by：

Wherein α is horizontal angle, and β is vertical angle.Then the area coverage model of survey station is represented by：

If measured target radial distance and vertical angle size are within the scope of survey station can be surveyed it is believed that survey station records the general of this point Rate is 1, if having one to exceed survey station in measured target radial distance or vertical angle size can survey scope then it is assumed that recording this point Probability is 0.

Described step 1) in,

Cost model to set up process as follows：

The present invention only considers the cost of investment when completing measuring task for the survey station, does not consider to run in measurement process This.After all survey stations are all deployed and finish, under every kind of layout, the cost consumption model of survey station is represented by：

O₃=C*N

In formula, C represents the cost of single survey station, and N represents the number of survey station.Suitable survey station number is selected in measured zone , so that region maximal cover, use cost is few simultaneously to meet measuring system precision, can be exchanged into multi-objective optimization question and asks for amount Solution.

According to survey station position error D and coverage F and survey station cost C, obtain survey station layout Model for Multi-Objective Optimization：

Min O₁=GDOP_pk

Min O₃=C*N.

Described step 2) in, due to object function dimension different with method for normalizing by the cloth of space measurement positioning system Office's multi-objective optimization question is converted into single-object problem and solves, and detailed process is as follows：

Wherein position error mathematical model is represented by：

In formula, PDOP_limIt is that the certainty of measurement that user proposes requires.

Area coverage model：

Use cost model:

In formula, N_actIt is actually used survey station number, N_maxIt is spendable survey station number.

The single goal that the layout optimization problem of therefore this space measurement positioning system is converted to following Weight coefficient is optimum Change problem：

Described step 3) in,

Using improved adaptive GA-IAGA, survey station layout Optimized model is solved, carry out as follows：

The parameter sets of object function are encoded into chromosome, and the chromosome population of random initializtion certain scale, i-th Being encoded to of individual survey station locus：

Wherein a and b represents coboundary and the lower boundary of measured zone respectively, and rand is that [0,1] spatially one is random Number；

According to the chromosome of coding, calculate corresponding fitness function FF：

FF=K₁O₁+K₂O₂+K₃O₃

According to fitness function value, using roulette selection, the i.e. selection strategy based on fitness ratio, individual i is selected The probability selected is:

In formula, FF_iIt is the adaptive value of i-th chromosome, M is colony's sum；

The chromosome being obtained according to select probability, improves self adaptation and intersects, crossover probability is：

In formula, F (t) is evolution decay factor,T is current evolutionary generation；T is total evolutionary generation；F is The big individuality of fitness value in individuality to be intersected；F' is the individual fitness value that will make a variation；f_avgFor colony's average fitness； f_maxFor colony's maximum adaptation degree.P_c1Equal to 0.9, P_c2Equal to 0.6, P_m1Equal to 0.1, P_m2Equal to 0.01.

Using Revised genetic algorithum, survey station layout Optimized model is solved so that having relatively in iteration initial stage algorithm Strong ability of searching optimum, with the increase of iterationses, the ability of searching optimum of algorithm declines, and local search ability strengthens, It is easy to obtain the globally optimal solution of survey station layout.

The invention has the advantages that：

(1) make full use of improved adaptive GA-IAGA to be intersected with variation generally according to ideal adaptation and evolutionary generation dynamic regulation Rate, thus improving global convergence and convergence rate, this improved adaptive GA-IAGA is incorporated into space measurement positioning system survey station cloth The solution of office's optimization problem；

(2) advantage in terms of optimization problem for the algorithm, genetic algorithm is incorporated into space measurement positioning system survey station The solution of layout optimization problem；

(3) establish rational survey station layout optimization aim model, realizing survey station optimization layout can be right under certain cost Comprehensive covering of tested region, and the requirement of certainty of measurement can be met；

(4) present invention can provide effective theoretical direction and ginseng for the rational deployment of angled type Intersection Measuring System survey station Examine, can be used for the fields such as accurate measurement in Large-Scale Equipment manufacture process, there is the features such as effect of optimization is good, and application is strong.

Brief description

Fig. 1 is the space measurement positioning system survey station layout optimization method flow chart based on improved adaptive GA-IAGA for the present invention； When Fig. 2 is to be carried out optimizing and carried out optimizing using the improved adaptive GA-IAGA of the application using standard genetic algorithm, to optimal adaptation Comparison diagram is illustrated in value iterative process emulation, and Fig. 2 (a1) is the simulation result of the improved adaptive GA-IAGA that two survey stations adopt the application Figure；Fig. 2 (a2) is the simulation result figure that two survey stations adopt standard genetic algorithm；

Fig. 2 (b1) is the simulation result figure of the improved adaptive GA-IAGA that three survey stations adopt the application；Fig. 2 (b2) is three surveys The simulation result figure stood using standard genetic algorithm；

Fig. 2 (c1) is the simulation result figure of the improved adaptive GA-IAGA that four survey stations adopt the application；Fig. 2 (c2) is four surveys The simulation result figure of standard genetic algorithm of standing.

Specific embodiments

The core concept of the present invention is space measurement positioning system survey station layout to be optimized with modeling and is lost based on improving The solution of propagation algorithm, the therefore present invention establish the position error of survey station, area coverage, the mathematical function relationship of use cost, I.e. survey station layout optimization aim mathematical model, in the case of considering different model dimensions differences, with method for normalizing by sky Between the layout optimization problem of measurement and positioning system be converted into single objective programming problem, finally carried out entirely using improved adaptive GA-IAGA Office's optimizing obtains optimal solution.

With reference to Fig. 1 algorithm flow chart, the space measurement positioning system survey station optimization side based on improved adaptive GA-IAGA for the present invention Method, implementation step is as follows：

1. set up survey station mathematical model：

1) system Model of locating error

Location estimation covariance matrix D is mainly determined by azimuth angle error propogator matrix H and measurement error covariance matrix Vm Fixed, its expression formula is：

D=(H^TVm^-1H)^-1(1)

According to matrix D, cloth station geometry is for any point P spatially_kGDOP (precision geometry dilution gfactor represents For：

Layout optimization to all survey stations is to reach the highest positioning precision to measured point, then above formula can be derived as：

O₁=GDOP_pk(3)

2) system area coverage model

Define cell site two optical plane inclination angle and be respectively φ₁And φ₂, make φ_max=max (φ₁,φ₂), then with Z axis it is Axis of symmetry, cone angle is 2 φ_maxTwo inverted cone up and down be cell site's laser plane scan blind spot.Receptor and cell site Distance is different, and the pulsewidth of light pulse will change, and therefore receptor would operate in limited distance range.

The measured target P dispensing at random on horizontal surface areas β ≡ 0_i, its coordinate is (x_i,y_i), for any survey station T_j, Measured target P_iWith any survey station T_jBetween Euclidean distance be：

Therefore only need to d (P_i,T_j) receptor effective working distance^From[LR_min,LR_max] between.And for having one Determine the plane domain of height H, the azimuth coverage that cell site can measure is represented by：

Wherein α is horizontal angle, and β is vertical angle.Then the area coverage model of survey station is represented by：

3) system use cost model

Only consider the cost of investment when completing measuring task for the survey station, do not consider operating cost in measurement process.Institute After having survey station to be all deployed and finish, under every kind of layout, the cost consumption model of survey station is represented by：

O₃=C*N (7)

In formula, C represents the cost of single survey station, and N represents the number of survey station.Suitable survey station number is selected in measured zone , so that region maximal cover, use cost is few simultaneously to meet measuring system precision for amount.Can be exchanged into multi-objective optimization question to ask Solution.

2. multiple objective function normalization

1) object function

The object function of the present invention mainly considers the position error of system, the coverage of system survey station and using into This, under meeting measuring system required precision so that region maximal cover use cost is few simultaneously.For the ease of optimize, need by This multiple target is converted into single-goal function, because the dimension of each target is different, needs each function normalization first.

2) normalization

③

For multi-objective optimization question, if giving each of which specific item scalar functions f (x_i) (i=1,2 ..., n) give weight coefficient K_i(i=1,2 ..., n), wherein K_iFor corresponding f (x_i) significance level (Σ K in multi-objective optimization question_i=1), then respectively Individual sub- object function f (x_i) linear weighted function and be expressed as:

Using f (X) as multi-objective optimization question evaluation function, then can be converted into single goal excellent for multi-objective optimization question Change problem, you can using the genetic algorithm for solving multi-objective optimization question of single object optimization.

The single goal that the layout optimization problem of therefore this space measurement positioning system is converted to following Weight coefficient is optimum Change problem：

Max f (x)=K₁O₁+K₂O₂+K₃O₃(12)

3. Revised genetic algorithum

1) improved crossover operator and mutation operator

Crossover probability P in genetic algorithm_cWith mutation probability P_mIntersection in algorithm and mutation operation are had vital Impact.But crossover probability and mutation probability are typically maintained constant in standard genetic algorithm calculating process, lead to algorithm local Convergence capabilities are poor, have such problems as precocity.For the problems referred to above, the present invention proposes a kind of Revised genetic algorithum, and this improvement is calculated The thought of method is:In the initial stage evolved and mid-term,Decay is simultaneously inconspicuous, individual less than average fitness Body always takes larger crossover probability and mutation probability, is so conducive to eliminating poor individuality；Individual higher than average fitness Body, its crossover probability and mutation probability can dynamically adjust according to the change of fitness.With the increase of evolutionary generation, hand over Fork and mutation probability slowly reduce, and to later stage of evolution, crossover probability and mutation probability reduce rapidly in the presence of decay factor, Thus ensureing that optimal solution is not destroyed.

Improved adaptive GA-IAGA intersects and mutation probability, and formula is as follows：

Wherein, F (t) is evolution decay factor,T is current evolutionary generation；T is total evolutionary generation；F is The big individuality of fitness value in individuality to be intersected；F' is the individual fitness value that will make a variation；f_avgFor colony's average fitness； f_maxFor colony's maximum adaptation degree.P_c1Equal to 0.9, P_c2Equal to 0.6, P_m1Equal to 0.1, P_m2Equal to 0.01.

2) realization of improved adaptive GA-IAGA

1. system survey station is position encoded

This patent takes floating-point encoding form, and the parameter sets of just object function are encoded into chromosome, and at random just The chromosome population of beginningization certain scale, being encoded to of i-th survey station locus：

Wherein a and b represents coboundary and the lower boundary of measured zone respectively, and rand is that [0,1] spatially one is random Number.

2. adaptive value calculates

According to the chromosome of coding, calculate corresponding fitness function F:

FF=K₁O₁+K₂O₂+K₃O₃(16)

Wherein, Σ K_i=1.

3. selection opertor

According to fitness function value, using roulette selection, the i.e. selection strategy based on fitness ratio, individual i is selected The probability selected is:

FF in formula_iIt is the adaptive value of i-th chromosome, M is colony's sum.

4. intersect and variation

Intersect and adopt improved genetic operator proposed by the present invention with mutation operator.

5. iteration ends criterion

The present invention determines whether to terminate iterative process using the maximum method terminating algebraically, and the termination algebraically of the present invention is 100.

According to the coding of survey station position, fitness function evaluation and selection opertor, crossover operator, the behaviour of mutation operator Make, through continuous iteration, obtain the globally optimal solution of survey station position, according to the globally optimal solution obtaining, fixed to space measurement Position system survey station is laid out.

Advantages of the present invention can be further illustrated by following emulation experiment：

1. experiment condition setting

It is assumed that deployment region is 16m*16m*8m, assume that survey station all works in the ideal situation, the work of every survey station simultaneously It is all 5m-20m with distance, each survey station angle measurement accuracy is 1 ", during emulation, weight coefficient is all set to 1/3, simultaneously by tested area Domain is divided into 50 points at equal intervals, to simulate tested region by these points, and these are put is called simulation measured point.The tool of propagation algorithm Body parameter setting：The scale of population is 20, maximum iteration time G_maxFor 100.

2. experiment content and result

This patent is respectively adopted standard genetic algorithm and improved adaptive GA-IAGA and different number survey station layout situations is imitated Very, simulation result is as follows：

In the case of two survey station layouts, one of survey station position is at (1.8975m, 9.2343m, 3.9292m), another Individual survey station position is at (14.8413m, 4.1144m, 6.211m).

In the case of three survey station layouts, optimum survey station position is respectively (1.9438m, 1.5566m, 7.4284m), (8.1586m,5.1908m,3.6678m),(15.4011m,5.8996m,5.9677m).

In the case of four survey station layouts, optimum survey station position is respectively (0.3735m, 14.3828m, 2.8796m), (10.8328m, 12.9841m, 5.4793m), (8.3125m, 9.4336m, 7.9247m), (1.8155m, 3.0321m, 5.6189m).

As can be seen from the above results, positioned at cloth station marginal area survey station be easier cover measurement target, reached by Need the purpose at cloth station, and be optimal location.

Genetic algorithm and improved adaptive GA-IAGA emulate adaptive optimal control and are worth the process of iteration situation, simulation result such as Fig. 2 institute Show, wherein Fig. 2 (a1) (a2) is the layout of 2 survey stations, Fig. 2 (b1) (b2) is the layout of 3 survey stations, and Fig. 2 (c1) (c2) is 4 The layout of survey station.From in figure it will be seen that in the case of two survey stations, when optimizing is carried out using standard genetic algorithm, calculating Method could be close to optimal solution in 60～70 generations, and corresponding object function maximum is 0.8092, using the improvement heredity of the application When algorithm carries out optimizing, algorithm reaches optimal solution in 10～20 generations, and corresponding object function maximum is 0.8227；Survey at three In the case of standing, when carrying out optimizing using standard genetic algorithm, algorithm could be close to optimal solution in 60～70 generations, corresponding target letter Number maximum is 0.7488, and when carrying out optimizing using the improved adaptive GA-IAGA of the application, algorithm reaches optimal solution in 10～20 generations, Corresponding object function maximum is 0.7497；In the case of four survey stations, when optimizing is carried out using standard genetic algorithm, algorithm Could be close to optimal solution in 80～90 generations, corresponding object function maximum is 0.6662, using the improved genetic algorithms of the application When method carries out optimizing, algorithm reaches optimal solution in 10～20 generations, and corresponding object function maximum is 0.6666.Emulate from above As can be seen that the improved adaptive GA-IAGA of this patent has fast convergence rate, so that optimal location can the features such as low optimization accuracy is high Rapidly found, reach the purpose of survey station global optimum.

Claims (5)

1. a kind of space measurement positioning system survey station layout intelligent optimization method it is characterised in that:In space measurement positioning system In, in order to obtain the survey station layout of optimum, set up by survey station position error, the multiple target number of coverage and use cost composition Learn relational model, i.e. survey station layout optimized mathematical model, with method for normalizing by the layout optimization of space measurement positioning system Problem is converted into single-object problem, and obtains optimum survey station layout using improved adaptive GA-IAGA；

Comprise the following steps that：

Step 1), in space orientation measuring system, set up survey station layout optimized mathematical model, including system position error mould Type, system ovelay range model, cost model；

Step 2), with method for normalizing, the layout multi-objective optimization question of space measurement positioning system to be converted into single goal excellent Change problem solving；

Step 3), using improved adaptive GA-IAGA, survey station layout Optimized model is solved；

Described step 3) in, using improved adaptive GA-IAGA, survey station layout Optimized model is solved, carry out as follows：

The parameter sets of object function are encoded into chromosome, and the chromosome population of random initializtion certain scale, i-th survey Being encoded to of stage space position：

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right]=\left[\begin{array}{c}a\\ a\\ a\end{array}\right]+\left[\begin{array}{c}b-a\\ b-a\\ b-a\end{array}\right]\·rand$

Wherein a and b represents coboundary and the lower boundary of measured zone respectively, and rand is [0,1] random number spatially；

According to the chromosome of coding, calculate corresponding fitness function FF：

FF=K₁O₁+K₂O₂+K₃O₃

According to fitness function value, using roulette selection, the i.e. selection strategy based on fitness ratio, individual i is selected Probability is:

$p_i=\frac{{\mathrm{FF}}_i}{\underset{i=1}{\overset{M}{\Σ}}{\mathrm{FF}}_i}$

In formula, FF_iIt is the adaptive value of i-th chromosome, M is colony's sum；

The chromosome being obtained according to select probability, improves self adaptation and intersects, mutation probability is：

$P_C=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{c1}-\frac{(P_{c1}-P_{c2})(f-f_{avg})}{f_{max}-f_{avg}}\&rsqb;& f\&GreaterEqual;f_{avg}\\ P_{c1}& f<f_{avg}\end{array}\right.$

$P_m=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{m1}-\frac{(P_{m1}-P_{m2})(f_{max}-f^{\&prime;})}{f_{max}-f_{avg}}\&rsqb;& f^{\&prime;}\&GreaterEqual;f_{avg}\\ P_{m1}& f^{\&prime;}<f_{avg}\end{array}\right.$

In formula, F (t) is evolution decay factor,T is current evolutionary generation；T is total evolutionary generation；F is to intersect Individuality in the big individuality of fitness value；F' is the individual fitness value that will make a variation；f_avgFor colony's average fitness；f_maxFor group Body maximum adaptation degree；P_c1Equal to 0.9, P_c2Equal to 0.6, P_m1Equal to 0.1, P_m2Equal to 0.01.

2. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 1 it is characterised in that: Described step 1) in,

System Model of locating error to set up process as follows：

In space orientation measuring system, including cell site, receptor, scale, omnidirectional's vector rod, its direct observed quantity is light Plane from zero scan to the time of measured point, under the local coordinate system of cell site, temporal information and horizontal angle and vertical angle Set up one-to-one functional relationship, therefore for each measurement of cell site, all have following formula to set up：

$\left\{\begin{array}{c}{\mathrm{\&alpha;}}_n=arctan\left(\frac{y_T-y_n}{x_T-x_n}\right)\\ {\mathrm{\&beta;}}_n=arctan\left(\frac{z_T-z_n}{R_n}\right)\\ R_n=\sqrt{{(x_T-x_n)}^2+(y_T-y_n)}\end{array}\right.$

T in formula_n=(x_n,y_n,z_n), n=1,2 ... N are expressed as n-th cell site's zero coordinate, P=(x_T,y_T,z_T) represent Point coordinates to be measured, R_nIt is the distance of floor projection range coordinate initial point under n-th cell site's coordinate system for the measured point, α_nRepresent The horizontal angle of n-th cell site, β_nRepresent the vertical angle of n-th cell site；

If m_niRepresent the i ＆ lt horizontal angle of n-th cell site and the measurement of vertical angle, m_iRepresent measured value, ε_niRepresent measurement by mistake Poor then have：

m_i=f_i(T₁,T₂,...T_n, P) and=m_ni+ε_ni, n=1,2 ... N

By f_iFunction, through Taylor series expansion and after removing all nonlinear components, obtains azimuth angle error propogator matrix H, represents For：

$H=\left[\begin{array}{c}{\left[\begin{array}{ccc}-\frac{(y_T-y_n)}{R_n^2}& \frac{(x_T-x_n)}{R_n^2}& 0\end{array}\right]}_{N\&times;3}\\ {\left[\begin{array}{ccc}-\frac{(x_T-x_n)(z_T-z_n)}{R_n{r}_n^2}& -\frac{(y_T-y_n)(z_T-z_n)}{R_n{r}_n^2}& \frac{R_n}{r_n^2}\end{array}\right]}_{N\&times;3}\end{array}\right]$

In formulaFor measured point to n-th cell site's initial point distance,For measured point floor projection to n-th cell site's initial point distance, now corresponding survey Amount error co-variance matrix is Δ m：

$\mathrm{\&Delta;}m=\left[\begin{array}{cc}diag{\left({\mathrm{\&sigma;}}_{\mathrm{\&alpha;}n}^2\right)}_{N\&times;N}& 0\\ 0& diag{\left({\mathrm{\&sigma;}}_{\mathrm{\&beta;}n}^2\right)}_{N\&times;N}\end{array}\right]$

In formulaWithRepresent horizontal angle and vertical angular measurement variance respectively；It is weighted processing according to covariance matrix, now Survey station position error D is：

D=(H^TΔm^-1H)^-1

According to matrix D, cloth station geometry is for any point P spatially_kPrecision geometry dilution gfactor GDOP be expressed as：

${\mathrm{GDOP}}_{p_k}=\sqrt{tr\left(D_{p_k}\right)}$

In formula,Represent P_kThe location estimation covariance matrix of point；

Layout optimization to all survey stations is to reach the highest positioning precision to measured point, then system Model of locating error For：

$O_1={\mathrm{GDOP}}_{p_k}.$

3. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 2 it is characterised in that: Described step 1) in, system ovelay range model to set up process as follows：

Define cell site two optical plane inclination angle and be respectively φ₁And φ₂, make φ_max=max (φ₁,φ₂)；It is then symmetrical with Z axis Axle, cone angle is 2 φ_maxTwo inverted cone up and down be cell site's laser plane scan blind spot；Receptor and cell site's distance Difference, the pulsewidth of light pulse will change, and therefore receptor would operate in limited distance range；

The measured target P dispensing at random on horizontal surface areas β ≡ 0_i, its coordinate is (x_i,y_i), for any survey station T_j, its seat It is designated as (x_j,y_j), then measured target P_iWith any survey station T_jBetween Euclidean distance be：

$d(P_i,T_j)=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}$

Therefore only need to d (P_i,T_j) receptor effective working distance [LR_min,LR_max] between, wherein LR_min,LR_max Represent the minimum of receptor, maximum range of receiving respectively；And the plane domain for height H, the azimuth that cell site can measure Range Representation is：

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\&lsqb;0,2\mathrm{\&pi;}\&rsqb;\\ \mathrm{\&beta;}=arctan(H/d(P_i,T_j))\end{array}\right.$

Wherein α is horizontal angle, and β is vertical angle；Then the area coverage model representation of survey station is：

If measured target radial distance and vertical angle size are within the scope of survey station can be surveyed it is believed that the probability that survey station records this point is 1, if having one to exceed survey station in measured target radial distance or vertical angle size can survey scope then it is assumed that recording the probability of this point For 0.

4. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 3 it is characterised in that: Described step 1) in,

Cost model to set up process as follows：

After all survey stations are all deployed and finish, under every kind of layout, the cost consumption model representation of survey station is：

O₃=C*N

In formula, C represents the cost of single survey station, and N represents the number of survey station；Select survey station quantity so that region in measured zone Maximal cover, use cost is few simultaneously to meet measuring system precision, is converted to multi-objective optimization question and solves；

According to survey station position error D and coverage and survey station cost, obtain survey station layout Model for Multi-Objective Optimization：

Min

Max

Min O₃=C*N.

5. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 4 it is characterised in that: Described step 2) in,

Because object function dimension is different, with method for normalizing by the layout multi-objective optimization question of space measurement positioning system It is converted into single-object problem to solve, detailed process is as follows：

Position error mathematical model is expressed as：

Wherein, PDOP_limIt is that the certainty of measurement that user proposes requires；

Area coverage model：

Use cost model:

$\begin{array}{cc}{O}_3=1-\frac{N_{act}}{N_{\max }}& (O_3\&Element;\&lsqb;0,1\&rsqb;)\end{array}$

In formula, N_actIt is actually used survey station number, N_maxIt is spendable survey station number；

The single objective programming that the layout optimization problem of therefore this space measurement positioning system is converted to following Weight coefficient is asked Topic：

Max f (x)=K₁O₁+K₂O₂+K₃O₃

In formula, K₁, K₂, K₃Represent weight, and